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Search: id:A081002
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| A081002 |
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Fibonacci(4n)+1, or Fibonacci(2n-1)*Lucas(2n+1). |
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1
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| 1, 4, 22, 145, 988, 6766, 46369, 317812, 2178310, 14930353, 102334156, 701408734, 4807526977, 32951280100, 225851433718, 1548008755921, 10610209857724, 72723460248142, 498454011879265, 3416454622906708, 23416728348467686
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75
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FORMULA
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a(n) = 8a(n-1)-8a(n-2)+a(n-3)
G.f.: (1-4x-2x^2)/(1-8x+8x^2-x^3); a(n)=sum{k=0..n, binomial(2n-k, 2k)2^(2n-3k)}; a(n)=sum{k=0..2n, binomial(4n-k-1, k)}+1-0^n. - Paul Barry (pbarry(AT)wit.ie), Jan 20 2005
a(n)=1-(1/5)*sqrt(5)*{[(7/2)-(3/2)*sqrt(5))^n+[(7/2)+(3/2)*sqrt(5)]^n}, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Dec 01 2008]
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MAPLE
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with(combinat): for n from 0 to 25 do printf(`%d, `, fibonacci(4*n)+1) od:
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CROSSREFS
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Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers).
Sequence in context: A104991 A027391 A134988 this_sequence A057834 A121394 A005039
Adjacent sequences: A080999 A081000 A081001 this_sequence A081003 A081004 A081005
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KEYWORD
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nonn,easy
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AUTHOR
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R. K. Guy (rkg(AT)cpsc.ucalgary.ca), Mar 01, 2003
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EXTENSIONS
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More terms and Maple code from James A. Sellers (sellersj(AT)math.psu.edu), Mar 01, 2003
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